MHB What is the significance of the recent discovery of the largest prime number?

[kaliprasad]

for details refer http://www.nytimes.com/2016/01/22/science/new-biggest-prime-number-mersenne-primes.html?_r=0

 

[Prove It]

Although this is very interesting, I have to wonder, what is the point in finding higher and higher primes, when it's been proven there are infinitely many of them, and as it says in the article, this prime is far too big to be of any practical use...?

 

[Deveno]

Although this is very interesting, I have to wonder, what is the point in finding higher and higher primes, when it's been proven there are infinitely many of them, and as it says in the article, this prime is far too big to be of any practical use...?

The size of the largest known prime provides a theoretical upper bound on number-theory based cryptography systems, and related bounds on the time necessary to break any such system using various "brute force" methods. One can think of this as the current limit to "how secure" a data lock can *possibly* be.

While most encryption systems do not have "need" for such a large number *currently*, the increasing speed and calculating capacity of electronic devices is growing so fast, that it is possible that we may reach this "soft limit" one day, and there will be no digital encryption system that cannot be broken by a sufficiently fast electronic device.

Or, maybe not, the exponential growth of digital devices may hit some other limit first that dramatically curtails the speed of future development. And very large primes may remain a curiosity that are seen as an archaic obsession of our time.

 

[Jameson]

I think it's a good benchmark of current computing power, like Deveno said. On Netflix I just rewatched a movie called Swordfish which was made in 2002 and they were talking about the difficulties of 128 bit encryption. I believe that is still not feasible to "brute force" crack, but I'm guessing secure government documents employ much larger keys.

I remember when I was a teenager I had just learned what GIMPS was and that you could get a cash prize at the time for discovering a new Mersenne Prime. It was my first time out of the country and right before it I installed the free program on my parents computer, asked them to please not turn off the computer or exit the program, and left. Called home a week later and... not prime. :( Remember the whole thing fondly though.